Factor v^2+4v+4

$v^{2} + 4 v + 4$

Step 1

Rewrite $4$ as $2^{2}$ .

$v^{2} + 4 v + 2^{2}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 v = 2 \cdot v \cdot 2$

Step 3

Rewrite the polynomial.

$v^{2} + 2 \cdot v \cdot 2 + 2^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = v$ and $b = 2$ .

${(v + 2)}^{2}$